### Nuprl Lemma : rotate-by-rotate-by

`∀[n,i,j:ℕ]. ∀[x:ℕn].  ((rotate-by(n;i) (rotate-by(n;j) x)) = (rotate-by(n;i + j) x) ∈ ℤ)`

Proof

Definitions occuring in Statement :  rotate-by: `rotate-by(n;i)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` apply: `f a` add: `n + m` natural_number: `\$n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` guard: `{T}` int_seg: `{i..j-}` ge: `i ≥ j ` lelt: `i ≤ j < k` and: `P ∧ Q` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` prop: `ℙ` true: `True` squash: `↓T` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` fun_exp: `f^n` primrec: `primrec(n;b;c)` compose: `f o g`
Lemmas referenced :  int_seg_wf nat_wf int_seg_properties nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermAdd_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_add_lemma int_term_value_var_lemma int_formula_prop_wf le_wf equal_wf fun_exp_wf fun_exp_add rotate_wf iff_weakening_equal compose_wf squash_wf true_wf iterate-rotate-rotate-by
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut hypothesis extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality setElimination rename hypothesisEquality sqequalRule isect_memberEquality axiomEquality because_Cache intEquality dependent_set_memberEquality addEquality productElimination dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality voidElimination voidEquality independent_pairFormation computeAll applyEquality imageElimination imageMemberEquality baseClosed equalityTransitivity equalitySymmetry independent_functionElimination universeEquality

Latex:
\mforall{}[n,i,j:\mBbbN{}].  \mforall{}[x:\mBbbN{}n].    ((rotate-by(n;i)  (rotate-by(n;j)  x))  =  (rotate-by(n;i  +  j)  x))

Date html generated: 2018_05_21-PM-08_18_47
Last ObjectModification: 2017_07_26-PM-05_52_16

Theory : general

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